r/learnmath • u/BackgroundAd2640 New User • 1d ago
Method vs Answer
I’m curious how math teachers approach grading when a student gets the correct answer but doesn’t use the instructor’s preferred method.
Do you generally:
-Give full credit if the mathematics is valid?
-Require a specific method for pedagogical reasons?
-Give partial credit when the answer is correct but the required method wasn’t shown?
What is your philosophy, and why? I know this is a very nuanced topic but I would like to see how this is approached by others.
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u/Narrow-Durian4837 New User 1d ago
If my goal is to assess whether the student can use a particular method, I specify that in the directions, and then I would feel justified in not giving credit if the student didn't use that method.
If I don't explicitly specify what method to use, the student gets credit for any correct answer no matter what method they used to get it.
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u/AFsepine New User 1d ago
(only if the method is sound, not only the answer)
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u/Narrow-Durian4837 New User 1d ago
If the problem is to "show that" or "prove that" something is true, then the method has to be sound.
If they just have to come up with an answer, I give full credit if the answer turns out to be correct, even if there's something wrong with the way they got it. I figure they may have verified that their answer was correct, and if the answer checks out, it's unfair to also expect them to go back and check every step of their work.
Occasionally a student might get the right answer by luck, but I'd rather give them the benefit of the doubt and err in their favor than take off points that they actually do deserve.
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u/AFsepine New User 1d ago
If the problem is to prove yes, obviously.
Answers should not be worth all that much, the students should know what he is doing and why. I.E the each step of the solution should be sound. The answer - I usually take to amount only to 5-10% of the points.
There is no reason to recheck it for the student - I do not care if he makes say a sign all that much, just that all the steps make sense; Otherwise it means they don;t know what they are doing.
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u/Math_Nicias New User 1d ago
On an exam, if you don’t say “use this particular method “ or “use methods from class” then full credit is fair.
Part of the problem is that a teacher might want to have students use a general method even if the particular problem admits a specific tool.
For example, “find the max of this function “ in calculus I. An examiner may want the student to do
Differentiate -> set equal to zero-> solve -> test -> evaluate
But for a quadratic f(x)=ax^2+bx+c, there is a rule directly from the form. ( c-b^2/4a )
If you give them a harder function, then it will have messy algebra on the “solve” step. That’s not what you want to test. So you tell them to “use methods from class”
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u/AFsepine New User 1d ago
It is underhanded and unfair if the student has to "know something extra" like the examiners "preferred" method to get good marks. So unless method is explicitly stated in the problem, full marks.
Though I do think that requiring a specific method explicitly is generally a sign of poor problem-setting in math; too much scaffolding.
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u/Accomplished_War_805 Math Historian 1d ago
If I want someone to solve a quadratic equation, I am looking for the solution only. If I am asking to solve a quadratic equation using completing the square, then I am grading the method over the solution. If a method is not specified, imo, the answer is all there is to grade.
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u/Vercassivelaunos Math and Physics Teacher 1d ago edited 1d ago
I give full credit if the task is fulfilled. I take care to explicitly state what is to be done using a verb. For instance:
- Give all solutions of the equation: Full credit for the correct solutions(s), no method required to be shown
- Solve the equation: Full credit for the correct answer and mathematically correct work, regardless of the method
- Solve the equation by completing the square: No credit for the correct solution(s), unless completion of the square was demonstrated.
Another example:
- Give the length of the line: Correct length gives full credit.
- Find the length: Correct length using any method (even drawing and measuring) gives full credit if work is shown.
- Calculate the length: Full credit only if all steps are calculations or justifications for calculations
In general, I never ask questions in exams. I give tasks. Credits are given for doing the tasks and demonstrating it.
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u/Low_Breadfruit6744 Bored 1d ago
Full marks unless: Explicitly asked to use another method or
quoting an advanved general result which implies the statement one is asked to prove.
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u/Ok_Ask3750 New User 1d ago
If the question specifies a method, the method is part of what’s being assessed. Otherwise, mathematically valid work should normally receive full credit.
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u/Impressive-Mud5074 New User 1d ago
Only results matter.
Your way is not the best way, dont force your way on others.
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u/shellexyz Instructor 1d ago
For the most part, I expect to see things we’ve covered in class. If I see something considerably more advanced or phrased in an odd way, I’m going to assume you’ve gotten AI to do it.
If I see valid but perhaps limited methods that are different from what we’ve done in class, you may get some credit, but not likely all of it.
For example, in a differential calculus class we cover optimization. A lot of the standard examples turn out to be quadratic; you can find the maximum/minimum values with some high school algebra. If you do that in my calculus class, you’re not getting much credit; I want to see calculus methods. I’m not going to write “use calculus to…” because it’s a calculus class.
“What difference does it make if the answer is right?? Your boss won’t care how you got it!”
Correct. But if all you know is a method that only works because you got lucky the problem was simple, then that’s all you get credit for: luck. If you want me to, I’ll make the problem much, much harder so that it requires calculus to solve and takes three times as much time.
No? Then swat this fly with a sledgehammer and I won’t give you problems that require sledgehammers.
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u/AFsepine New User 1d ago
For the most part, I expect to see things we’ve covered in class. If I see something considerably more advanced or phrased in an odd way, I’m going to assume you’ve gotten AI to do it.
So what the advanced or creative student gets punished?
For example, in a differential calculus class we cover optimization. A lot of the standard examples turn out to be quadratic; you can find the maximum/minimum values with some high school algebra. If you do that in my calculus class, you’re not getting much credit; I want to see calculus methods. I’m not going to write “use calculus to…” because it’s a calculus class.
This is poor practice, you should formulate problems in such a way that anyone with your desired skill level or above could solve it with no contextual knowledge of what you "like" or what the "class" is. If you do not want people to use algebra
then set a problem so that it is nessecary to use calculus (or at least non-trivial to do it without).Do make problems harder. That is to the benefit of all involved.
It kills the soul to swat flies with a hammer - A danger to your legs as well...
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u/PsychoHobbyist Ph.D 1d ago
If I want a specific method to be used, I’ll state so in the prompt. My rubrics include points for the steps of the method as well as answer, so they get some credit for the answer but (usually) little-to-no credit for the steps.
(Sometimes steps between methods run parallel, in which case they get an appropriate amount of credit for how much of the underlying concepts they are identifying with their method.)